The present invention relates to a method and a device for determining geometric data of a conical measurement object.
For quality control of industrially produced workpieces, the workpieces are often examined or measured by means of coordinate measuring machines in order to check if the workpieces correspond to the specifications. For this purpose, a workpiece to be measured is placed in the measurement volume of a coordinate measuring machine. The coordinate measuring machine has a measuring head, often in the form of a tactile probe head, by means of which defined measurement points of the workpiece are scanned. Due to the defined position of the measurement object within the measurement volume, spatial coordinates of the measurement point can then be determined by means of the position of the measuring head within the measurement volume. When the spatial coordinates are determined at a plurality of measurement points, it is possible to determine geometric data of the measurement object, such as the circumference or the diameter of a bore or the length of a side.
However, measurement errors of different causes are superposed on each measurement value. Some measurement errors can be predicted, for example on the basis of a change in room temperature. Other measurement errors, however, are unknown. Moreover, each workpiece has individual manufacturing tolerances. Coordinate measuring technology is therefore facing the challenge of acquiring unknown manufacturing tolerances of the workpieces even when the superposed and at least partially unknown measurement errors are of the same order of magnitude.
When a measurement object is measured by means of a coordinate measuring machine at a plurality of measurement points, a “point cloud” of spatial coordinates is obtained as a result. If these points are connected notionally, a metrological image of the measurement object is obtained. This metrological image differs from the ideal measurement object as a result of the measurement errors and as a result of the manufacturing tolerances. Since the determination of the geometric data on the metrological image can vary substantially depending on which measurement points are used, an ideal substitute element matching the “point cloud” as good as possible is often determined. The substitute element allows the geometric data to be determined with higher reproducibility and a better basis for comparisons.
There are several substitute elements that are more or less well suited depending on the shape of the measurement object and on the geometric data being sought. Known substitute elements are Gaussian elements, minimum elements, envelope elements and inscribed elements. In the case of a Gaussian element, the sum of the squares of the deviations between measurement points and the ideal substitute element is minimized. Therefore, there is exactly one Gaussian substitute element for each specific point cloud. The same holds true for the minimum element, in the case of which the deviation of the maximum absolute value between substitute element and any desired measurement point is minimized. Gaussian and minimum elements can be uniquely determined both for “open” measurement objects or measurement regions (for example straight line or plane) and for “closed” measurement objects (for example circle, ball, cylinder).
The envelope element is the smallest possible substitute element that encloses all the measurement points. The inscribed element is the largest possible substitute element where all the measurement points lie outside the substitute element. Since the envelope and the inscribed substitute elements touch at least some measurement points, they are often called fitting or tangential substitute elements.
Envelope and inscribed elements are well suited for determining geometric data such as location, orientation, diameter, length and other pairing dimensions. In the case of conical measurement objects, however, envelope or inscribed substitute elements could only be determined if additional conditions (secondary conditions), such as the cone angle of the envelope or inscribed cone, had been defined in advance. Such secondary conditions, however, complicate the comparability of the measurements since the secondary conditions would always need to be considered.
DE 10 2005 030 274 A1 suggested a method and a device by means of which the envelope and inscribed cones of a conical measurement object can be uniquely determined without specifying a cone angle as secondary condition. The document proposes to use the point cloud initially to determine a first conical substitute element, in particular a minimum cone. Subsequently, the cone angle of the minimum cone is used to transform the measurement points of the point cloud such that the transformed measurement points form a substantially cylindrical intermediate element. A cylindrical substitute element in the form of an envelope cylinder or inscribed cylinder was determined for this intermediate element. In the next step, the longitudinal axis of the cylindrical substitute element is determined, and a further coordinate transformation of the measurement points is performed such that the cone apex of the originally determined minimum cone lies on the longitudinal axis of the cylindrical substitute element. Following thereupon, this minimum cone is displaced on the longitudinal axis of the cylindrical substitute element until the condition of envelope or inscription is fulfilled.
Thus, in the case of this method and the corresponding device, the envelope or inscribed cone is determined via the detour of a tangential cylindrical substitute element. The cone angle of the minimum cone is used as cone angle. The method leads to a uniquely determined substitute element, even without a prior secondary condition, and therefore avoids the above-mentioned disadvantages. However, this method is time-consuming and computation intensive, because a plurality of coordinate transformations and the determination of two substitute elements has to be carried out.
DE 198 21 372 A1 discloses a coordinate measuring machine and a method for controlling it, with a plurality of spatial coordinates being determined at a plurality of measurement points. Parameters of geometric elements, such as a circle or a plane, are stored in the controller of the coordinate measuring machine in order to define the measurement points to be scanned on the measurement object. The document proposes to store these parameters with reference to a respectively dedicated coordinate system of the geometric elements. This document, however, does not indicate a solution for the above-mentioned problems in the context of determining tangential substitute elements for conical measurement objects.